Given the following two statements :

$\left( S _{1}\right):( q \vee p ) \rightarrow( p \leftrightarrow \sim q )$ is a tautology.

$\left( S _{2}\right): \sim q \wedge(\sim p \leftrightarrow q )$ is a fallacy.

Then

Statement $\left( {p \wedge q} \right) \to \left( {p \vee q} \right)$ is

Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then

Let $*, \square \in\{\wedge, \vee\}$ be such that the Boolean expression $(\mathrm{p} * \sim \mathrm{q}) \Rightarrow(\mathrm{p} \square \mathrm{q})$ is a tautology. Then :

Dual of $(x \vee y) \wedge (x \vee 1) = x \vee (x \wedge y) \vee y$ is